Step 1: Classify the triangle by angles and sides

1. By Angles:
   The triangle has a right angle (90°) as shown in the diagram. Therefore, it is classified as a right triangle.

2. By Sides:
   The sides are given as 3 m and 4 m for the legs. Using the Pythagorean theorem:
   $c = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{m}$ Since all three sides have different lengths (3 m, 4 m, and 5 m), the triangle is classified as a scalene triangle.

Step 2: Find the area

The formula for the area of a triangle is:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
Here, the base is 3 m, and the height is 4 m:
$\text{Area} = \frac{1}{2} \times 3 \times 4 = 6 \, \text{m}^2$

Final Answer:

1. Classification:

   • By angles: Right triangle.
   • By sides: Scalene triangle.

2. Area:
   $6 \, \text{m}^2$

Would you like more detailed explanations or help with related concepts?
Here are 5 related questions you might find helpful:

1. How do you verify a triangle is scalene using side lengths?
2. What is the Pythagorean theorem and how does it apply to right triangles?
3. How can you classify triangles when only angles are given?
4. What are real-world applications of calculating triangle areas?
5. How would the area change if one side is doubled?

Tip: Always check if the triangle is a right triangle before applying the Pythagorean theorem.